
where the second inequality follows from Jensen's inequality
[1]} and the convexity of
\(\log \left(a_1e^{x_1}+a_2e^{x_2}\right)\)  in \((x_1,x_2)\)  for \(a_1,a_2\ge 0\) .
Taking logarithm on both sides of (REF ) proves the desired inequality
(REF ).
